Multi-criteria group decision-making method based on total distance and BWM with spatial information in Hesitant Pythagorean fuzzy environment

The processing method of fuzzy information is a critical element in multi-criteria group decision-making (MCGDM). The hesitant Pythagorean fuzzy set (HPFS) has a higher capacity in express the uncertainty of human inherent preference. A composite weighted mathematical programming model with prospect theory and best-worst method (BWM) is proposed to solve the uncertainty of criterion weight acquisition and decision-makers (DMs) psychological behavior under the HPF environment. The decision-making process is as follows: Firstly, a novel spatial distance measurement method is designed which considers the extension space of HPFSs space by five parameters under the HPF environment. Secondly, the optimal criteria weights model minimizes the total distance between the alternatives and the HPF positive ideal solution (HPFPIS), as well as minimizes the consistency ratio of BWM. Thirdly, we propose the prospect decision matrix by the prospect theory and optimal weights, then use the ordered weighted average operator under the normal distribution to calculate the weight of DMs and rank the decision alternatives. Finally, an example is illustrated here, sensitivity and reliability, and comparative analysis are conducted to verify the effectiveness of the proposed method.